{
  "id": 1188,
  "curve_key": "74827201:-6235781680801",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1558900",
    "7217210000"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    8
  ],
  "naive_height": 58.92265011403625,
  "faltings_height": 2.9680074578597258,
  "conductor": "681870",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "17",
    "191"
  ],
  "discriminant": "-22260420972518400000000",
  "regulator": "2.69524188279579459181578435925299618507240",
  "points": [
    [
      "-2128",
      "31052"
    ],
    [
      "-1750",
      "68600"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Found by a rational-parameter search of the Kubert-Tate family for torsion 8, at t=5/17. In y^2+(1-c)xy-by=x^3-bx^2 the parameters are defined by b=(2*t-1)*(t-1);c=b/t; Converted to the global minimal model; PARI/GP ellrank returned bounds [2,2]. The 2 supplied points and the torsion subgroup are independently certified by the site.",
  "created_at": "2026-09-23 21:40:07",
  "updated_at": "2026-09-23 21:40:07"
}